csp-variants · pachet2001-harmonization-constraints

The combinatorial problem arises when one has to produce harmonizations with an imposed, fixed voice. In this case, the harmonization problem naturally becomes a finite domain constraint satisfaction problem: each note to find may be considered as a variable whose domain is the range of the corresponding voice (soprano, alto, tenor, bass). The harmonic rules may then be considered as constraints [...]. Traditional exercises in composition classes include: Melody imposed (soprano), compose the three other voices. Unfigured bass: the bass is imposed; compose the three other voices. [...] Figured bass: the bass part is imposed, as well as figures indicating the nature of the chord on top of each note of the bass. [...] It used to correspond to an actual practice of harpsichord players, who had to play - in real time - chords that satisfied the bass voice, the figures, and a sung melody. Two-voice problems. A melody is imposed, find the bass only.